Mathematical logics refer to the systematic study of mathematical reasoning and its applications. There are several synonyms that are used to describe this field of study, including symbolic logic, formal logic, mathematical logic, and deductive logic. Symbolic logic refers to the representation of logical operations using symbols and abbreviations. Formal logic emphasizes the study of logical reasoning, which is based on formal mathematical models. Mathematical logic, on the other hand, explores the intersections between logic and mathematics, including the use of mathematical methods to prove theorems. Deductive logic focuses on reasoning from given premises to a valid conclusion by following strict rules of inference.